Late-time critical behavior of local string-like observables under quantum quenches

In recent times it has been observed that signatures of equilibrium quantum criticality surprisingly show up in many-body systems which are manifestly far from equilibrium. We explore such scenarios in interacting spin systems subject to a quench and develop a robust method to systematically probe ground state critical physics through nonequilibrium post-quench dynamics. Analyzing late-time behavior of finite string-like observables, we find emerging sharp signatures of equilibrium criticality. Specifically, these observables accurately detect equilibrium critical points and universal scaling exponents after long times following a quench. This happens despite the fact that the analyzed systems are strongly chaotic/ergodic and is interestingly due to a strong memory of the initial conditions retained by these observables after quench. We find that our results can also be used to explain critical signatures in post-quench domain formation, seen in a recent experiment with trapped ion quantum simulators.